On rational reciprocity
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- by Charles Helou
- Proc. Amer. Math. Soc. 108 (1990), 861-866
- DOI: https://doi.org/10.1090/S0002-9939-1990-1007498-2
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Abstract:
A method for deriving "rational" $n$th power reciprocity laws from general ones is described. It is applied in the cases $n = 3,4,8$, yielding results of von Lienen, Burde, Williams.References
- Klaus Burde, Ein rationales biquadratisches Reziprozitätsgesetz, J. Reine Angew. Math. 235 (1969), 175–184 (German). MR 241354, DOI 10.1515/crll.1969.235.175 G. Eisenstein, Mathematische Werke I and II, Chelsea, 1975.
- Kenneth F. Ireland and Michael I. Rosen, A classical introduction to modern number theory, Graduate Texts in Mathematics, vol. 84, Springer-Verlag, New York-Berlin, 1982. Revised edition of Elements of number theory. MR 661047
- Horst von Lienen, Reelle kubische und biquadratische Legendre-Symbole, J. Reine Angew. Math. 305 (1979), 140–154 (German). MR 518858, DOI 10.1515/crll.1979.305.140
- Kenneth S. Williams, A rational octic reciprocity law, Pacific J. Math. 63 (1976), no. 2, 563–570. MR 414467
Bibliographic Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 108 (1990), 861-866
- MSC: Primary 11A15; Secondary 11R04
- DOI: https://doi.org/10.1090/S0002-9939-1990-1007498-2
- MathSciNet review: 1007498